Approximating a norm by a polynomial
Functional Analysis
2007-05-23 v1 Metric Geometry
Abstract
We prove that for any norm |*| in the d-dimensional real vector space V and for any odd n>0 there is a non-negative polynomial p(x), x in V of degree 2n such that p^{1/2n}(x) < |x| < c(n,d) p^{1/2n}(x), where c(n,d)={n+d-1 choose n}^{1/2n}. Corollaries and polynomial approximations of the Minkowski functional of a convex body are discussed.
Cite
@article{arxiv.math/0105069,
title = {Approximating a norm by a polynomial},
author = {Alexander Barvinok},
journal= {arXiv preprint arXiv:math/0105069},
year = {2007}
}
Comments
5 pages